How to achieve more physically accurate motion in the game engine?
All of the answers here so far do not quite fix your problem. it is actually quite easy to fix. Radish Has the right idea (using linear velocity set to Add). This answer also expands (and says more clearly) what StealthyRobot said in his answer. (Although the numbers which he gave there do not work as expected)

First you need to use linear velocity with the settings local and add enabled.  (I assume you already have this) 



Now we can fix the overshoot problem. to do this increase the damping on the Translation for your character.



If you are using Torque to steer, also set Rotation dampening.

It also might be useful to view this question

Realistic Jet Flight

You can see it working here



If you had trouble following that, (hopefully you did not) or if you just want to see it working, feel free to take apart/play with the blend file.